Enhancement of void growth model for the anisotropic ductile metal

VIETNAM NATIONAL UNIVERSITY – HO CHI MINH CITY HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY NGUYỄN HỮU HÀO ENHANCEMENT OF VOID GROWTH MODEL FOR THE ANISOTROPIC DUCTILE METAL DISSERTATION HO CHI MINH CITY 2019 VIETNAM NATIONAL UNIVERSITY – HO CHI MINH CITY HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY NGUYỄN HỮU HÀO ENHANCEMENT OF VOID GROWTH MODEL FOR THE ANISOTROPIC DUCTILE METAL Major: Engineering Mechanics Code: 62 52 01 01 Independent reviewer 1: Assoc Prof Dr Nguyễn Đức Toàn Independent reviewer 2: Dr Trương Quang Tri Reviewer 1: Assoc Prof Dr Nguyễn Xuân Hùng Reviewer 2: Assoc Prof Dr Nguyễn Văn Hiếu Reviewer 3: Assoc Prof Dr Bùi Công Thành SCIENCE ADVISORS: Assoc Prof Dr Vũ Cơng Hịa Dr Nguyễn Ngọc Trung DECLARATION OF ORIGINALITY I confirm that this dissertation is my own work and that any material from published or unpublished work from others is appropriately referenced Signature: Nguyễn Hữu Hào i COPYRIGHT DECLARATION The copyright of this dissertation rests with the author and is made available under a Ho Chi Minh City University of Technology, VNU-HCM license Researchers are free to copy, distribute or transmit the dissertation on the condition that they attribute it, that they not use it for commercial purposes and that they not alter, transform or build upon it For any reuse or redistribution, researchers must make clear to others the license terms of this work ii ABSTRACT The aim of work presented in this dissertation was to produce the improvement of the existing void growth-based damage models used for the ductile fracture analysis and prediction of sheet metals, which are subjected plastic deformation The original metal material is usually containing the second phase particles or/and inclusions Once the metallic material under deformation lead to the nucleation, growth and coalescence of voids that it is root of ductile damage The main objective of this work was enhancement of micro-void growth-based damage model to predict ductile fracture behavior of sheet aluminum alloys, typical for civil structures with anisotropic properties and their implementation in user-defined material subroutine (VUMAT) The explicit finite element code has been chosen for implementation of new material models Constitutive model with anisotropic yield criterion, damage growth and failure mechanism has been developed and implemented into ABAQUS/Explicit software The second important aspect of this dissertation was performance of tensile experiments in three different orientations of materials for identification of mechanical behavior of high strength sheet aluminum alloys AA6061-T6 The results from these tests allowed derivation of material constants for constitutive models and help to have a better understanding of anisotropic material behavior The tensile tests were also used to validate the implementation and accuracy of constitutive material models The constitutive models were developed within the general framework of ductile damage mechanics Coupling of the quadratic yield function Hill48 with damage model based on micro-mechanical and continuum damage mechanics (CDM) theories has been chosen to suit the anisotropic behavior of sheet material The validation of the constitutive models has been performed by numerical simulations of tensile, deep drawing and Nakajima tests The micro-crack and fracture initiation, crack path and forming limit diagram (FLD) are predicted using these constitutive models iii ACKNOWLEDGEMENT I would like to express my sincere gratitude to my supervisors, Assoc Pro Dr Vũ Cơng Hịa and Dr Nguyễn Ngọc Trung for their guidance, technical support, and helpful discussions during this research The knowledge and efforts of my colleagues in our group was a valuable source of inspiration and success Finally, I would like to express my profound gratitude to my wife and my parents for their support and encouragement throughout my education and professional career iv CONTENTS DECLARATION OF ORIGINALITY i COPYRIGHT DECLARATION ii ABSTRACT iii ACKNOWLEDGEMENT iv CONTENTS v LIST OF FIGURES viii LIST OF TABLES xi LIST OF ACRONYMS xii NOMENCLATURE xiii CHAPTER INTRODUCTION The research motivation .1 The research objectives Research methodology The contributions of dissertation .5 Dissertation outline CHAPTER DUCTILE FRACTURE OF METALLIC MATERIAL Ductile damage mechanism of metallic material .7 Microscopic void nucleation 2.2.1 Experimental investigations 2.2.2 Void nucleation models 10 2.2.2.1 Argon model 10 2.2.2.2 Beremin model 10 2.2.2.3 Needleman and Tvergaard model 11 2.2.2.4 Bouaziz and Maire model 11 Microscopic void growth 12 2.3.1 Experimental investigations 12 2.3.2 Void growth model 13 2.3.2.1 McClintock model 13 2.3.2.2 Rice and Tracey model .14 v 2.3.2.3 Gurson-Tvergaard-Needleman (GTN) model 15 2.3.2.4 N L Dung model .17 Void coalescence leads to microscopic crack 20 2.4.1 Experimental investigations 20 2.4.2 Void coalescence models 22 2.4.2.1 McClintock model 22 2.4.2.2 Brown and Embury model 22 2.4.2.3 Tvergaard and Needleman model 23 2.4.2.4 Void coalescence model due to shear mechanism 24 2.4.2.5 N L Dung model .25 CHAPTER DUCTILE FRACTURE MODELLING 27 The continuum damage mechanics (CDM) model 27 3.1.1 The constitutive equations of void growth based CDM model 27 3.1.2 An extension of the void growth model for shear damage 34 The porous ductile model .37 CHAPTER NUMERICAL IMPLEMENTATION OF THE DUCTILE DAMAGE MODELS…………………………………………………………………………… 42 Overview of the vectorized user material (VUMAT) subroutine 42 Numerical implementation of CDM model 43 Numerical implementation of the porous ductile model 46 4.3.1 Constitutive equations .46 4.3.2 Implemented procedure .51 4.3.3 Updating the stress state and solution dependent variables 53 4.3.4 The derivatives of Dung-Hill48 model 55 Verification of user-defined material subroutine .58 4.4.1 Verification by the unit elements 58 4.4.1.1 Geometries and boundary conditions 58 4.4.1.2 The material properties .59 4.4.1.3 The results using CDM model 60 Effect of softening exponent β 60 g Effect of critical damage parameter Dcrit 61 vi 4.4.1.4 The results using porous ductile model 62 Effect of hardening exponent 62 Effect of Lankford’s coefficients .63 Effect of shear coefficient 64 4.4.2 Verification by tensile and deep drawing tests of AA6016-T4 aluminum alloy…………………………………………………………………………… 66 4.4.2.1 The material parameters .66 4.4.2.2 Tensile test 66 4.4.2.3 Deep drawing 68 CHAPTER IDENTIFICATION OF MATERIAL PARAMETERS 71 Experimental work 71 Calibration of the material parameters for the damage models 78 5.2.1 The calibrated approach and procedure 78 5.2.2 CDM model 80 5.2.3 Porous ductile model 81 CHAPTER DUCTILE FRACTURE PREDICTION OF AA6061-T6 ALUMINUM ALLOY……………………………………………………………………………… 84 The tensile tests 84 6.1.1 Geometries, mesh and boundary conditions .84 6.1.2 Ductility prediction 85 6.1.3 Crack initiation and propagation prediction 89 6.1.4 Ductile fracture strain prediction 98 Forming limit diagram (FLD) prediction 99 CHAPTER CONCLUSIONS AND FUTURE WORK 105 The overall conclusions 105 The recommends for future work 106 LIST OF PUPLICATIONS 127 REFERENCES 129 vii LIST OF FIGURES Figure 1.1 The ductile fracture under forming process of plastic deformation [1, 2] .1 Figure 1.2 Exact prediction of ductile fracture by numerical simulation [2, 4] Figure 2.1 Ductile fracture mechanism of metallic material: a) specimen, b) the process of void nucleation, growth and coalescence during plastic strain evolution [32] Figure 2.2 Micro-void nucleation inside AA6061 aluminum alloy specimens: (a) interface deboning and (b) particle cracking [34] Figure 2.3 Second phase and non-metallic particles in alloy steel [40] Figure 2.4 Void nucleation in double phase steel: (a) 2D view, (b) 3D view [41] .10 Figure 2.5 Microscopic graph of AA6061 alloy [53]: (a) microscopic structure in an unetched condition; (b) void growth in notched specimen under uniaxial tension .12 Figure 2.6 The void nucleation (red color) by Zirconia inclusions (light blue color): (a) homogeneous deformation; (b) localized deformation [55] 13 Figure 2.7 McClintock’s void growth model (a) solid contains the cylindrical voids; (b) unit cell model [9] 14 Figure 2.8 Rice and Tracey void growth model [10] .15 Figure 2.9 The Gurson void growth model: a) arbitrary voids in cubic solid, b) a spherical void in spherical solid [18] 16 Figure 2.10 Circular cylindrical void in the cylindrical solid [18] 17 Figure 2.11 N L Dung void growth model: a) cylindrical void; b) ellipsoidal void; c) void distribution in matrix material [60] 18 Figure 2.12 The first void coalescence mode: a) Benzerga [65] and b, c ) Weck [64] 21 Figure 2.13 Second mode of void coalescence a) and b) Benzerga [67] and c) Pardoen et al [68]) 21 Figure 2.14 Third void coalescence mode a) and b) Weck [64]; c) Benzerga [67] 21 Figure 3.1 Illustration of rotation of coordinates system about 3-axis 32 Figure 3.2 Illustration of void shear mechanism [25] 35 Figure 3.3 The yield surface presentation of the Dung-Hill48 and pure Hill48 models in normalized principal stress space 39 Figure 4.1 Geometrical illustration of the “cutting-plane” algorithm 45 Figure 4.2 Presentation of normal distribution function of void nucleation respect to equivalent plastic strain 49 Figure 4.3 Unit element (a) uniaxial tension and (b) simple shear 58 Figure 4.4 True stress-strain curve 59 viii DAIHeceuoc crATp.HCM ceNGHoAxA uer cHUNcnia vrEr NAM rnUONi o4i ngc nAcu KHoA DOc l4p- is ao- H4nhphric NHaNXEr LUANAX rmN Si CuanghiOncuu sinh: Nguy6nHiru Hdo T6n d€ tdi: Mo r6ng m6 hinh tbngtruong 16h6ng cho kim loai bi6n d4ngd6ob6t ding hucmg Chuy0nngd.nh: Co hgck! thuat H9 tdn ngucrinhin xet: Chircdanh:Ph6gi6osu Luong Hong SAm Chuy6nngi,nh: Co ch6t4o m6y Co quanc6ngt6c: TrucrngDH TrdnD4i Nghia Nambd nhi6m:2017 Md s5: 62.52.02.01 Hgc vi: Ti6nsi Nim bAovQ:2006 /t V xrnN Nrr,iNxET SWcAnthitit vir tfnh thli sq, f nghia khoa hgc vi thr;c ti6n cria 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